10 SCIENTIFIC HIGHLIGHT OF THE MONTH Many-body perturbation theory using the density-functional concept

Many-body perturbation theory (MBPT) oers a convenient framework for the calcula- tion of electronic excitations. In principle, all kinds of electronic excitations (i.e., neutral or involving a change in particle number) are accessible, and the physics that has to be included is relatively well understood. Also time-dependent density-functional theory (TDDFT) al- lows one in principle to describe excitations, at a a priori lower computational cost. However, in that case it is more dicult to design good approximations for the exchange-correlation contribution, since one does not work in the physically intuitive quasi-particle picture. More- over, only neutral excitations are accessible. In order to combine the advantages of both approaches, we propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Variations of many-body quantities upon excitation are expressed through variations with respect to the density. In this way, instead of the usual four-point integral equation for the polarizability (namely, the Bethe-Salpeter equation), we obtain a two-point one (i.e., like in TDDFT), that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. With the help of numerical results, we discuss the consequences of exchange-correlation contributions to the response for optical spectra and for the band gap of bulk silicon and solid argon.